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triangle adc is greater than ade; but ‘the equilateral 
triangle may be proved greater than adc from the hrft 
cafcj and confequently greater than ade. D. 
p R o P o s I T I o N II. 
equilateral triangle deferibed about a circle is befs than 
any other triangle that can be deferibed about the fame 
circle. Fig. 3. 
LET the equilateral triangle aec be deferibed about 
the circle niK, and let the triangle bdg be fuj^pofed lefs 
than the equilateral triangle. Draw the line af parallel 
to Bc, then the triangles afe, egc, are fimilar ; for the 
oppofite angles aef, gec, are equal, as likewife the angle 
afe to the angle egc ; the lines af and gc being pai'allel, 
and falling upon the fame line fg, the angles afe and 
EGC are therefore equal, and the tides ae, ec, fubtending 
equal angles, ai'e homologous ; but the tide of the equi- 
lateral triangle ac being equally divided at i, the line 
ae is greater than ec, and confequently the triangle afe 
is larger than the triangle egc; and the triangle dae 
riiuch larger than egc: therefore, in the triangles dbg 
and ABC the part abge being common the whole trian- 
gle dbg is larger than the equilateral triangle. £, D. 
Whatever other triangles can be deferibed about a cir- 
cle, may be demonflrated to be larger than an equilateral 
triangle deferibed about the fame circle, vq^on the fame 
principles as the preceding. 
p R o p c- 
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